{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.6 Q学習で迷路を攻略"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 使用するパッケージの宣言\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\yutar\\Anaconda3\\envs\\rl_env\\lib\\site-packages\\matplotlib\\cbook\\deprecation.py:107: MatplotlibDeprecationWarning: Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.\n",
      "  warnings.warn(message, mplDeprecation, stacklevel=1)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 初期位置での迷路の様子\n",
    "\n",
    "# 図を描く大きさと、図の変数名を宣言\n",
    "fig = plt.figure(figsize=(5, 5))\n",
    "ax = plt.gca()\n",
    "\n",
    "# 赤い壁を描く\n",
    "plt.plot([1, 1], [0, 1], color='red', linewidth=2)\n",
    "plt.plot([1, 2], [2, 2], color='red', linewidth=2)\n",
    "plt.plot([2, 2], [2, 1], color='red', linewidth=2)\n",
    "plt.plot([2, 3], [1, 1], color='red', linewidth=2)\n",
    "\n",
    "# 状態を示す文字S0～S8を描く\n",
    "plt.text(0.5, 2.5, 'S0', size=14, ha='center')\n",
    "plt.text(1.5, 2.5, 'S1', size=14, ha='center')\n",
    "plt.text(2.5, 2.5, 'S2', size=14, ha='center')\n",
    "plt.text(0.5, 1.5, 'S3', size=14, ha='center')\n",
    "plt.text(1.5, 1.5, 'S4', size=14, ha='center')\n",
    "plt.text(2.5, 1.5, 'S5', size=14, ha='center')\n",
    "plt.text(0.5, 0.5, 'S6', size=14, ha='center')\n",
    "plt.text(1.5, 0.5, 'S7', size=14, ha='center')\n",
    "plt.text(2.5, 0.5, 'S8', size=14, ha='center')\n",
    "plt.text(0.5, 2.3, 'START', ha='center')\n",
    "plt.text(2.5, 0.3, 'GOAL', ha='center')\n",
    "\n",
    "# 描画範囲の設定と目盛りを消す設定\n",
    "ax.set_xlim(0, 3)\n",
    "ax.set_ylim(0, 3)\n",
    "plt.tick_params(axis='both', which='both', bottom='off', top='off',\n",
    "                labelbottom='off', right='off', left='off', labelleft='off')\n",
    "\n",
    "# 現在地S0に緑丸を描画する\n",
    "line, = ax.plot([0.5], [2.5], marker=\"o\", color='g', markersize=60)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 初期の方策を決定するパラメータtheta_0を設定\n",
    "\n",
    "# 行は状態0～7、列は移動方向で↑、→、↓、←を表す\n",
    "theta_0 = np.array([[np.nan, 1, 1, np.nan],  # s0\n",
    "                    [np.nan, 1, np.nan, 1],  # s1\n",
    "                    [np.nan, np.nan, 1, 1],  # s2\n",
    "                    [1, 1, 1, np.nan],  # s3\n",
    "                    [np.nan, np.nan, 1, 1],  # s4\n",
    "                    [1, np.nan, np.nan, np.nan],  # s5\n",
    "                    [1, np.nan, np.nan, np.nan],  # s6\n",
    "                    [1, 1, np.nan, np.nan],  # s7、※s8はゴールなので、方策はなし\n",
    "                    ])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 方策パラメータtheta_0をランダム方策piに変換する関数の定義\n",
    "\n",
    "\n",
    "def simple_convert_into_pi_from_theta(theta):\n",
    "    '''単純に割合を計算する'''\n",
    "\n",
    "    [m, n] = theta.shape  # thetaの行列サイズを取得\n",
    "    pi = np.zeros((m, n))\n",
    "    for i in range(0, m):\n",
    "        pi[i, :] = theta[i, :] / np.nansum(theta[i, :])  # 割合の計算\n",
    "\n",
    "    pi = np.nan_to_num(pi)  # nanを0に変換\n",
    "\n",
    "    return pi\n",
    "\n",
    "# ランダム行動方策pi_0を求める\n",
    "pi_0 = simple_convert_into_pi_from_theta(theta_0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 初期の行動価値関数Qを設定\n",
    "\n",
    "[a, b] = theta_0.shape  # 行と列の数をa, bに格納\n",
    "Q = np.random.rand(a, b) * theta_0 * 0.1\n",
    "# *theta0をすることで要素ごとに掛け算をし、Qの壁方向の値がnanになる\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ε-greedy法を実装\n",
    "\n",
    "\n",
    "def get_action(s, Q, epsilon, pi_0):\n",
    "    direction = [\"up\", \"right\", \"down\", \"left\"]\n",
    "\n",
    "    # 行動を決める\n",
    "    if np.random.rand() < epsilon:\n",
    "        # εの確率でランダムに動く\n",
    "        next_direction = np.random.choice(direction, p=pi_0[s, :])\n",
    "    else:\n",
    "        # Qの最大値の行動を採用する\n",
    "        next_direction = direction[np.nanargmax(Q[s, :])]\n",
    "\n",
    "    # 行動をindexに\n",
    "    if next_direction == \"up\":\n",
    "        action = 0\n",
    "    elif next_direction == \"right\":\n",
    "        action = 1\n",
    "    elif next_direction == \"down\":\n",
    "        action = 2\n",
    "    elif next_direction == \"left\":\n",
    "        action = 3\n",
    "\n",
    "    return action\n",
    "\n",
    "\n",
    "def get_s_next(s, a, Q, epsilon, pi_0):\n",
    "    direction = [\"up\", \"right\", \"down\", \"left\"]\n",
    "    next_direction = direction[a]  # 行動aの方向\n",
    "\n",
    "    # 行動から次の状態を決める\n",
    "    if next_direction == \"up\":\n",
    "        s_next = s - 3  # 上に移動するときは状態の数字が3小さくなる\n",
    "    elif next_direction == \"right\":\n",
    "        s_next = s + 1  # 右に移動するときは状態の数字が1大きくなる\n",
    "    elif next_direction == \"down\":\n",
    "        s_next = s + 3  # 下に移動するときは状態の数字が3大きくなる\n",
    "    elif next_direction == \"left\":\n",
    "        s_next = s - 1  # 左に移動するときは状態の数字が1小さくなる\n",
    "\n",
    "    return s_next\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Q学習による行動価値関数Qの更新\n",
    "\n",
    "\n",
    "def Q_learning(s, a, r, s_next, Q, eta, gamma):\n",
    "\n",
    "    if s_next == 8:  # ゴールした場合\n",
    "        Q[s, a] = Q[s, a] + eta * (r - Q[s, a])\n",
    "\n",
    "    else:\n",
    "        Q[s, a] = Q[s, a] + eta * (r + gamma * np.nanmax(Q[s_next,: ]) - Q[s, a])\n",
    "\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Q学習で迷路を解く関数の定義、状態と行動の履歴および更新したQを出力\n",
    "\n",
    "\n",
    "def goal_maze_ret_s_a_Q(Q, epsilon, eta, gamma, pi):\n",
    "    s = 0  # スタート地点\n",
    "    a = a_next = get_action(s, Q, epsilon, pi)  # 初期の行動\n",
    "    s_a_history = [[0, np.nan]]  # エージェントの移動を記録するリスト\n",
    "\n",
    "    while (1):  # ゴールするまでループ\n",
    "        a = a_next  # 行動更新\n",
    "\n",
    "        s_a_history[-1][1] = a\n",
    "        # 現在の状態（つまり一番最後なのでindex=-1）に行動を代入\n",
    "\n",
    "        s_next = get_s_next(s, a, Q, epsilon, pi)\n",
    "        # 次の状態を格納\n",
    "\n",
    "        s_a_history.append([s_next, np.nan])\n",
    "        # 次の状態を代入。行動はまだ分からないのでnanにしておく\n",
    "\n",
    "        # 報酬を与え,　次の行動を求めます\n",
    "        if s_next == 8:\n",
    "            r = 1  # ゴールにたどり着いたなら報酬を与える\n",
    "            a_next = np.nan\n",
    "        else:\n",
    "            r = 0\n",
    "            a_next = get_action(s_next, Q, epsilon, pi)\n",
    "            # 次の行動a_nextを求めます。\n",
    "\n",
    "        # 価値関数を更新\n",
    "        Q = Q_learning(s, a, r, s_next, Q, eta, gamma)\n",
    "\n",
    "        # 終了判定\n",
    "        if s_next == 8:  # ゴール地点なら終了\n",
    "            break\n",
    "        else:\n",
    "            s = s_next\n",
    "\n",
    "    return [s_a_history, Q]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "エピソード:1\n",
      "0.33695783349641584\n",
      "迷路を解くのにかかったステップ数は676です\n",
      "エピソード:2\n",
      "0.09800995966053788\n",
      "迷路を解くのにかかったステップ数は14です\n",
      "エピソード:3\n",
      "0.09791232661824678\n",
      "迷路を解くのにかかったステップ数は18です\n",
      "エピソード:4\n",
      "0.09373145367281005\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:5\n",
      "0.09250125578394505\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:6\n",
      "0.09157216378601814\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:7\n",
      "0.09062211846852089\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:8\n",
      "0.0896387103252213\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:9\n",
      "0.08861021709396733\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:10\n",
      "0.0875262501519074\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:11\n",
      "0.08637815285133413\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:12\n",
      "0.08515920972816424\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:13\n",
      "0.08386471417151692\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:14\n",
      "0.08249193272840702\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:15\n",
      "0.08103999643025925\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:16\n",
      "0.07950974311037037\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:17\n",
      "0.07790352941437567\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:18\n",
      "0.07622502690288072\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:19\n",
      "0.07447901314845165\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:20\n",
      "0.07267116590403111\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:21\n",
      "0.07080786615306545\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:22\n",
      "0.06889601404734899\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:23\n",
      "0.06694286031601429\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:24\n",
      "0.06495585462023931\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:25\n",
      "0.06294251147607507\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:26\n",
      "0.06091029372453988\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:27\n",
      "0.05886651305389909\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:28\n",
      "0.05681824674066879\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:29\n",
      "0.054772269545764\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:30\n",
      "0.052734999557598417\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:31\n",
      "0.05071245669606911\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:32\n",
      "0.04871023256481488\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:33\n",
      "0.04673347035141928\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:34\n",
      "0.04478685351610606\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:35\n",
      "0.042874602070793466\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:36\n",
      "0.04100047532554485\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:37\n",
      "0.039167780063303625\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:38\n",
      "0.03737938319226247\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:39\n",
      "0.03563772801512982\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:40\n",
      "0.0339448533435755\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:41\n",
      "0.0323024147724445\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:42\n",
      "0.030711707510698683\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:43\n",
      "0.02917369024357419\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:44\n",
      "0.02768900957260012\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:45\n",
      "0.026258024646585887\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:46\n",
      "0.024880831657365876\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:47\n",
      "0.02355728792900269\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:48\n",
      "0.022287035378472986\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:49\n",
      "0.021069523169803372\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:50\n",
      "0.019904029422487923\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:51\n",
      "0.018789681869120334\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:52\n",
      "0.017725477386872357\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:53\n",
      "0.016710300353082963\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:54\n",
      "0.015742939797159017\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:55\n",
      "0.014822105339579394\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:56\n",
      "0.013946441924356234\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:57\n",
      "0.013114543364184161\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:58\n",
      "0.012324964727989274\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:59\n",
      "0.011576233608951214\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:60\n",
      "0.010866860317587324\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:61\n",
      "0.01019534704938685\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:62\n",
      "0.009560196079986483\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:63\n",
      "0.008959917043182775\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:64\n",
      "0.008393033348366719\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:65\n",
      "0.007858087794390012\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:66\n",
      "0.007353647436583288\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:67\n",
      "0.006878307762769875\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:68\n",
      "0.006430696232754052\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:69\n",
      "0.006009475234031281\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:70\n",
      "0.005613344504422191\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:71\n",
      "0.005241043070085549\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:72\n",
      "0.004891350744940959\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:73\n",
      "0.0045630892350194685\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:74\n",
      "0.0042551228886746895\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:75\n",
      "0.003966359130999408\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:76\n",
      "0.0036957486181991017\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:77\n",
      "0.0034422851451395564\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:78\n",
      "0.003205005336789357\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:79\n",
      "0.002982988151882915\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:80\n",
      "0.0027753542248091234\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:81\n",
      "0.0025812650695137274\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:82\n",
      "0.0023999221670997217\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:83\n",
      "0.002230565956815478\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:84\n",
      "0.0020724747482360195\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:85\n",
      "0.0019249635706810597\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:86\n",
      "0.0017873829742647285\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:87\n",
      "0.0016591177954323744\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:88\n",
      "0.0015395858984186273\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:89\n",
      "0.001428236902737745\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:90\n",
      "0.0013245509056067917\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:91\n",
      "0.0012280372070851975\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:92\n",
      "0.00113823304468752\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:93\n",
      "0.0010547023433052916\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:94\n",
      "0.0009770344854084234\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:95\n",
      "0.0009048431057477879\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:96\n",
      "0.0008377649140651755\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:97\n",
      "0.0007754585487091958\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:98\n",
      "0.0007176034634801542\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:99\n",
      "0.000663898849534772\n",
      "迷路を解くのにかかったステップ数は4です\n",
      "エピソード:100\n",
      "0.0006140625937295363\n",
      "迷路を解くのにかかったステップ数は4です\n"
     ]
    }
   ],
   "source": [
    "# Q学習で迷路を解く\n",
    "\n",
    "eta = 0.1  # 学習率\n",
    "gamma = 0.9  # 時間割引率\n",
    "epsilon = 0.5  # ε-greedy法の初期値\n",
    "v = np.nanmax(Q, axis=1)  # 状態ごとに価値の最大値を求める\n",
    "is_continue = True\n",
    "episode = 1\n",
    "\n",
    "V = []  # エピソードごとの状態価値を格納する\n",
    "V.append(np.nanmax(Q, axis=1))  # 状態ごとに行動価値の最大値を求める\n",
    "\n",
    "while is_continue:  # is_continueがFalseになるまで繰り返す\n",
    "    print(\"エピソード:\" + str(episode))\n",
    "\n",
    "    # ε-greedyの値を少しずつ小さくする\n",
    "    epsilon = epsilon / 2\n",
    "\n",
    "    # Q学習で迷路を解き、移動した履歴と更新したQを求める\n",
    "    [s_a_history, Q] = goal_maze_ret_s_a_Q(Q, epsilon, eta, gamma, pi_0)\n",
    "\n",
    "    # 状態価値の変化\n",
    "    new_v = np.nanmax(Q, axis=1)  # 状態ごとに行動価値の最大値を求める\n",
    "    print(np.sum(np.abs(new_v - v)))  # 状態価値関数の変化を出力\n",
    "    v = new_v\n",
    "    V.append(v)  # このエピソード終了時の状態価値関数を追加\n",
    "\n",
    "    print(\"迷路を解くのにかかったステップ数は\" + str(len(s_a_history) - 1) + \"です\")\n",
    "\n",
    "    # 100エピソード繰り返す\n",
    "    episode = episode + 1\n",
    "    if episode > 100:\n",
    "        break\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
       "css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<div class=\"animation\" align=\"center\">\n",
       "    <img id=\"_anim_img254a6de2af7047bc9bcc4deb46c9cda9\">\n",
       "    <br>\n",
       "    <input id=\"_anim_slider254a6de2af7047bc9bcc4deb46c9cda9\" type=\"range\" style=\"width:350px\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           onchange=\"anim254a6de2af7047bc9bcc4deb46c9cda9.set_frame(parseInt(this.value));\"></input>\n",
       "    <br>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.previous_frame()\">\n",
       "        <i class=\"fa fa-step-backward\"></i></button>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.reverse_animation()\">\n",
       "        <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.pause_animation()\"><i class=\"fa fa-pause\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.play_animation()\"><i class=\"fa fa-play\"></i>\n",
       "        </button>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.next_frame()\"><i class=\"fa fa-step-forward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim254a6de2af7047bc9bcc4deb46c9cda9.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
       "  <form action=\"#n\" name=\"_anim_loop_select254a6de2af7047bc9bcc4deb46c9cda9\" class=\"anim_control\">\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"once\" checked> Once </input>\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"loop\" > Loop </input>\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"reflect\" > Reflect </input>\n",
       "  </form>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img254a6de2af7047bc9bcc4deb46c9cda9\";\n",
       "    var slider_id = \"_anim_slider254a6de2af7047bc9bcc4deb46c9cda9\";\n",
       "    var loop_select_id = \"_anim_loop_select254a6de2af7047bc9bcc4deb46c9cda9\";\n",
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       "\"\n",
       "  frames[100] = \"\\\n",
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       "BlqSgjLQkhSUgZakoP4fOnDgjFktcuIAAAAASUVORK5CYII=\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim254a6de2af7047bc9bcc4deb46c9cda9 = new Animation(frames, img_id, slider_id, 200.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 状態価値の変化を可視化します\n",
    "# 参考URL http://louistiao.me/posts/notebooks/embedding-matplotlib-animations-in-jupyter-notebooks/\n",
    "from matplotlib import animation\n",
    "from IPython.display import HTML\n",
    "import matplotlib.cm as cm  # color map\n",
    "\n",
    "\n",
    "def init():\n",
    "    # 背景画像の初期化\n",
    "    line.set_data([], [])\n",
    "    return (line,)\n",
    "\n",
    "\n",
    "def animate(i):\n",
    "    # フレームごとの描画内容\n",
    "    # 各マスに状態価値の大きさに基づく色付きの四角を描画\n",
    "    line, = ax.plot([0.5], [2.5], marker=\"s\",\n",
    "                    color=cm.jet(V[i][0]), markersize=85)  # S0\n",
    "    line, = ax.plot([1.5], [2.5], marker=\"s\",\n",
    "                    color=cm.jet(V[i][1]), markersize=85)  # S1\n",
    "    line, = ax.plot([2.5], [2.5], marker=\"s\",\n",
    "                    color=cm.jet(V[i][2]), markersize=85)  # S2\n",
    "    line, = ax.plot([0.5], [1.5], marker=\"s\",\n",
    "                    color=cm.jet(V[i][3]), markersize=85)  # S3\n",
    "    line, = ax.plot([1.5], [1.5], marker=\"s\",\n",
    "                    color=cm.jet(V[i][4]), markersize=85)  # S4\n",
    "    line, = ax.plot([2.5], [1.5], marker=\"s\",\n",
    "                    color=cm.jet(V[i][5]), markersize=85)  # S5\n",
    "    line, = ax.plot([0.5], [0.5], marker=\"s\",\n",
    "                    color=cm.jet(V[i][6]), markersize=85)  # S6\n",
    "    line, = ax.plot([1.5], [0.5], marker=\"s\",\n",
    "                    color=cm.jet(V[i][7]), markersize=85)  # S7\n",
    "    line, = ax.plot([2.5], [0.5], marker=\"s\",\n",
    "                    color=cm.jet(1.0), markersize=85)  # S8\n",
    "    return (line,)\n",
    "\n",
    "\n",
    "#　初期化関数とフレームごとの描画関数を用いて動画を作成\n",
    "anim = animation.FuncAnimation(\n",
    "    fig, animate, init_func=init, frames=len(V), interval=200, repeat=False)\n",
    "\n",
    "HTML(anim.to_jshtml())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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